Abstract: Using the information of the function value near the latest iteration point, we estimated simplex gradient of the point and calculated BarzilaiBorwein (BB) stepsize of the current point. We proposed an updating strategy of the grid stepsize based on adaptive BB stepsize, which could effectively solve the problem that the grid stepsize dropped too fast. Combined with the new updating strategy, we proposed a new direct search algorithm. The numerical results show that the algorithm has a great improvement in stability and efficiency.

Key words: direct search, simplex gradient, conjugate gradient, adaptive BarzilaiBorwein (BB) stepsize